Calendar: 1874-1875 Page 545

GENERAL LITERATURE AND SCIENCE 545 ference in then the rectangle contained by Β BE equals the rectangle contained by BC BD 11 If triangle be inscribed in circle and from any point on the circumference of the circle perpendiculars be drawn on the sides of the triangle the feet of these perpendiculars lie in the same straight line 12 If from any point without circle there be drawn two straight lines one to cut the circle and the other to meet it and if the rectangle contained by the whole line which cuts the circle and the part of it without the circle be equal to the square on the line which meets the circle the line which meets the circle shall touch it 13 To inscribe circle in given triangle Show how to inscribe circle in given quadrant 14 To inscribe regular hexagon in given circle 15 Tofindamean proportional between twogiven straight lines Find by geometrical construction an arithmetic geometric and harmonic mean between two straight lines 16 Similar triangles are to one another in the duplicate ratio of their homologous sides 17 If the vertical angle of triangle be bisected by straight line which also cuts the base the rectangle contained by the sides of tbe triangle is equal to the rectangle contained by the segments of the bases together with tbe square on the straight line which bisects the angle 18 If two sides of triangle be unequal the sum of the greater side and the perpendicular upon it from the opposite angle is greater than the sum of the smaller side and the perpendicular upon it from the opposite angle 19 One vertex of rectangle moves about fixed point and the two adjacent vertices move along given circle find the locus of the remaining vertex 20 Draw the lines represented by tbe equation y2 2xy sec and find the angle between them 21 Draw the lines 2x 3y -f- 3χ 4y and find the distance of their point of intersection from the line 2'x Μ Μ